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We develop efficient binary (i.e., 1-bit) and multi-bit coding schemes for estimating the scale parameter of $\alpha$-stable distributions. The work is motivated by the recent work on one scan 1-bit compressed sensing (sparse signal…

Methodology · Statistics 2016-02-02 Ping Li

We show how to utilize machine learning approaches to improve sliding window algorithms for approximate frequency estimation problems, under the ``algorithms with predictions'' framework. In this dynamic environment, previous…

Data Structures and Algorithms · Computer Science 2024-09-19 Rana Shahout , Ibrahim Sabek , Michael Mitzenmacher

The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…

Data Structures and Algorithms · Computer Science 2021-09-06 Vladimir Braverman , Viska Wei , Samson Zhou

One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…

Machine Learning · Statistics 2015-11-10 Ahmed El Alaoui , Michael W. Mahoney

We consider the problem of estimating the mean of a symmetric log-concave distribution under the constraint that only a single bit per sample from this distribution is available to the estimator. We study the mean squared error as a…

Information Theory · Computer Science 2023-08-29 Alon Kipnis , John C. Duchi

In this paper, we take into consideration quantile estimation in data stream models, where every item in the data stream is a key-value pair. Researchers sometimes aim to estimate per-key quantiles (i.e. quantile estimation for every…

Data Structures and Algorithms · Computer Science 2025-12-01 Jiarui Guo , Qiushi Lyu , Yuhan Wu , Haoyu Li , Zhaoqian Yao , Yuqi Dong , Xiaolin Wang , Bin Cui , Tong Yang

A central problem in data streams is to characterize which functions of an underlying frequency vector can be approximated efficiently. Recently there has been considerable effort in extending this problem to that of estimating functions of…

Data Structures and Algorithms · Computer Science 2018-10-25 Vladimir Braverman , Stephen R. Chestnut , Robert Krauthgamer , Yi Li , David P. Woodruff , Lin F. Yang

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Machine Learning · Computer Science 2021-04-08 Danica J. Sutherland , Jeff Schneider

Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath…

Data Structures and Algorithms · Computer Science 2012-05-14 Ping Li

Many datasets such as market basket data, text or hypertext documents, and sensor observations recorded in different locations or time periods, are modeled as a collection of sets over a ground set of keys. We are interested in basic…

Databases · Computer Science 2009-03-05 Edith Cohen , Haim Kaplan

Identifying heavy hitters and estimating the frequencies of flows are fundamental tasks in various network domains. Existing approaches to this challenge can broadly be categorized into two groups, hashing-based and competing-counter-based.…

Data Structures and Algorithms · Computer Science 2024-06-25 Rana Shahout , Michael Mitzenmacher

The Basic Counting problem [1] is one of the most fundamental and critical streaming problems of sliding window queries over data streams. Given a stream of 0's and 1's, the purpose of this problem is to estimate the number of 1's in the…

Data Structures and Algorithms · Computer Science 2019-12-10 Shuhao Sun , Dagang Li

Pairwise alignment of DNA sequencing data is a ubiquitous task in bioinformatics and typically represents a heavy computational burden. A standard approach to speed up this task is to compute "sketches" of the DNA reads (typically via…

Information Theory · Computer Science 2021-07-12 Ilan Shomorony , Govinda M. Kamath

Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this…

Machine Learning · Statistics 2019-11-05 Yang Shi , Animashree Anandkumar

We present a method for image-based crowd counting, one that can predict a crowd density map together with the uncertainty values pertaining to the predicted density map. To obtain prediction uncertainty, we model the crowd density values…

Computer Vision and Pattern Recognition · Computer Science 2020-10-06 Viresh Ranjan , Boyu Wang , Mubarak Shah , Minh Hoai

Crucial performance metrics of a caching algorithm include its ability to quickly and accurately learn a popularity distribution of requests. However, a majority of work on analytical performance analysis focuses on hit probability after an…

Networking and Internet Architecture · Computer Science 2020-04-02 Archana Bura , Desik Rengarajan , Dileep Kalathil , Srinivas Shakkottai , Jean-Francois Chamberland-Tremblay

We study the approximation of expectations $\E(f(X))$ for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms,…

Numerical Analysis · Mathematics 2018-02-15 Michael B. Giles , Mario Hefter , Lukas Mayer , Klaus Ritter

This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…

Computation · Statistics 2012-11-20 Peter Clifford , Ioana A. Cosma

With the exponentially growing Internet traffic, sketch data structure with a probabilistic algorithm has been expected to be an alternative solution for non-compromised (non-selective) security monitoring. While facilitating counting…

Cryptography and Security · Computer Science 2025-03-18 Seungsam Yang , Seyed Mohammad Mehdi Mirnajafizadeh , Sian Kim , Rhongho Jang , DaeHun Nyang

Given a stream $p_1, \ldots, p_m$ of items from a universe $\mathcal{U}$, which, without loss of generality we identify with the set of integers $\{1, 2, \ldots, n\}$, we consider the problem of returning all $\ell_2$-heavy hitters, i.e.,…

Data Structures and Algorithms · Computer Science 2015-11-03 Vladimir Braverman , Stephen R. Chestnut , Nikita Ivkin , David P. Woodruff